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A127221 a(n) = 2^n*pentanacci(n) or (2^n)*A023424(n-1). 3
2, 12, 56, 240, 992, 3648, 14464, 57088, 224768, 883712, 3471360, 13651968, 53682176, 211075072, 829915136, 3263102976, 12830244864, 50447253504, 198353354752, 779904614400, 3066503888896, 12057176965120, 47407572189184, 186401664532480, 732912043425792 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,4,8,16,32).

FORMULA

a(n) = Trace of matrix [({{2,2,2,2,0},{2,0,0,0,0},{0,2,0,0,0),{0,0,2,0,0},{0,0,0,2,0})^n].

a(n) = 2^n * Trace of matrix [({{1,1,1,1,1},{1,0,0,0,0},{0,1,0,0,0},{0,0,1,0,0},{0,0,0,1,0)^n].

G.f.: -2*x*(1 +4*x +12*x^2 +32*x^3 +80*x^4)/(-1 +2*x +4*x^2 +8*x^3 +16*x^4 +32*x^5). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009

a(n) = 2*a(n-1)+4*a(n-2)+8*a(n-3)+16*a(n-4)+32*a(n-5). - Colin Barker, Sep 02 2013

MATHEMATICA

Table[Tr[MatrixPower[2*{{1, 1, 1, 1, 1}, {1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}}, x]], {x, 1, 20}]

LinearRecurrence[{2, 4, 8, 16, 32}, {2, 12, 56, 240, 992}, 50] (* G. C. Greubel, Dec 19 2017 *)

PROG

(PARI) x='x+O('x^30); Vec(-2*x*(1 +4*x +12*x^2 +32*x^3 +80*x^4)/(-1 +2*x +4*x^2 +8*x^3 +16*x^4 +32*x^5)) \\ G. C. Greubel, Dec 19 2017

(MAGMA) I:=[2, 12, 56, 240, 992]; [n le 5 select I[n] else 2*Self(n-1) + 4*Self(n-2) + 8*Self(n-3) + 16*Self(n-4) + 32*Self(n-5): n in [1..30]]; // G. C. Greubel, Dec 19 2017

CROSSREFS

Cf. A087131, A127210, A127211, A127212, A127213, A127214, A127216, A001648, A127220, A127222.

Cf. A023424, A074048.

Sequence in context: A127216 A006659 A194771 * A020522 A037130 A181298

Adjacent sequences:  A127218 A127219 A127220 * A127222 A127223 A127224

KEYWORD

nonn,easy

AUTHOR

Artur Jasinski, Jan 09 2007

EXTENSIONS

G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009

Definition corrected by R. J. Mathar, Sep 17 2009

More terms from Colin Barker, Sep 02 2013

STATUS

approved

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Last modified August 22 07:17 EDT 2019. Contains 326172 sequences. (Running on oeis4.)